A specific question is - can members of different genus have offspring?For example, family Felidae has 14 genus, including Felis (housecat) and Panthera (lion, tiger, jaguar, leopard). Obviously Felis and Panthera cannot mate, but is there something that prevents cats of similar size from different genus to mate?

Are there specific rules that govern when an organism is placed in a separate genus?Do you know of a book or website that discusses that in general?

They aren't supposed to, but biology is a science full of exceptions to rules (I have mice in my lab that appear to be the product of separate mouse Families). And the rules for genus-level and higher vary - I think the commonest rule for any group is that they all share a common ancestor that also qualifies to be in that group, based upon characteristics or genetics.